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How to prove the following identity

  • Thread starter amitech
  • Start date
3
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1. Homework Statement

e_j=g_(jk)e^k

where e_j is a covariant vector base
e^k is a a contravariant vector base
g_(jk) is the covariant metric

2. Homework Equations



3. The Attempt at a Solution
 

HallsofIvy

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What is the definition of the "covariant metric". How do you go from a covariant to the corresponding contravariant vector and vice-versa?
 
3
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Hi, by saying "covariant metic" I mean writing the metric in its covariant form - basically g(contra)=[g(cov)]^(-1)
you can use the metric to lower/raise an index on a vector component but here e_j and e^k are not components but the actual unit vectors.
 
3
0
Hi, by saying "covariant metic" I mean writing the metric in its covariant form - basically g(contra)=[g(cov)]^(-1)
you can use the metric to lower/raise an index on a vector component but here e_j and e^k are not components but the actual unit vectors.
 

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